Lemma 4.5 ([1]}, Lemma 3.14) 

Suppose that for a family \(\mathcal {F}\)  of subgroups of a group \(G\)  there is a tree model \(T\)  for \(E_{\mathcal {F}}G\) . Let \(S_e\)  be the stabilizer of the edge \(e\in T\)  and \(S_v\)  the stabilizer of a vertex. Let \(N\)  be a coefficient module. Then \(H_i^{\mathcal {F}}(G,N)=0\)  for \(i>1\)  and there is an exact sequence:
\( 0\rightarrow H_1^{\mathcal {F}}(G,N)\rightarrow \bigoplus _{[e]} N(G/S_e) \rightarrow \bigoplus _{[v]} N(G/S_v)\rightarrow H_0^{\mathcal {F}}(G,N)\rightarrow 0,\) 
